Laser scanning, computed tomography and other non-contact measurement technologies have been increasingly used to measure manufactured parts. Through recent developments, these three-dimensional measuring technologies have become more accurate and the speed of data acquisition has increased dramatically. In fact, some sensors are capable of producing more than 200,000 measured points per second. This high performance and fast processing speed provide a large amount of information about the surface being measured, but they also cause a major problem for handling these increasingly large data clouds. That is, it tends to be difficult to extract accurate and useful information within a reasonable amount of time from the large amount of data.
Fundamentally, there are two major reasons for obtaining information about the part. The first reason is known as reverse engineering, in which information is collected about an unknown geometry and a CAD model representing the parts is then created. The second reason for obtaining this information is to verify tolerance compliance. That is, when a desired geometry is known, such as in the form of a drawing or a CAD model, it is desirable to obtain measurements of a manufactured part to prove that the part conforms to a specified tolerance zone as established by the known desired geometry. These two uses of the measurement information require very different approaches during data reduction processes. In the first use, the final goal of the information is to produce a smooth mathematical surface that simulates the part. This creation of the mathematical surface requires averaging of the data points. In contrast, the second use, that is, for verification of tolerance compliance, requires that the measured data points be fitted or oriented to the nominal geometry and compared to its tolerance zone. In the second use, averaging cannot be used because it is important to know about the actual surface of the part for compliance, not a smooth rendering of that surface.
Many methods for data reduction are conventionally known, but all are based on some sort of averaging technique. For example, known techniques include arithmetical average, median, and geometrical average. However these averaging techniques are not able to preserve the surface information adequately for a comparison to a tolerance zone.
In one conventional example, an original data cloud is reduced by dividing it into grids, either two dimensional or three dimensional, and by sampling a representative point from each grid. This representative point may be the center of gravity, the simple average, the median point, or something else. The grids in these conventional methods may be uniform or non-uniform. In another known technique, data is tessellated into triangular planes. When one triangle substitutes multiple points, data reduction is achieved. The size of the triangle is based on a given threshold for the residual deviations (error) of the points to which the triangular plane is best fit. If the error exceeds the threshold, the triangle is subdivided into smaller triangles until the threshold is met. Another technique is to fit mathematical surfaces to the data cloud and the surfaces are later used to generate smaller numbers of substitution points. Yet another technique is shown in U.S. Pat. No. 7,420,555, which describes a method of mapping multiple points into regular cubes, called voxels, for the purpose of faster visualization. Each voxel is represented by its average point and all points mapped to the voxel have the same attributes. However, each of these techniques is an averaging technique.
While all of these mentioned techniques are suitable for the purpose of reverse engineering with the respective advantages and drawbacks, none of them is suitable for verification for tolerance compliance. In the case of tolerance compliance, the part is measured to make a yes/no decision as whether or not the feature is in tolerance. Using the conventional techniques described above, bad parts may be accepted because each of those techniques leads to underestimation of errors. By averaging substitution of points, the volume information of the original points is not being preserved and only the average information is being kept. When fitting data to a tolerance zone, it is the extreme points and not the average points that determine the result of the evaluation.
An analogy would be to use the least squares averaging method to calculate the sizes of a piston and a cylinder which have real form errors for the purposes of determining whether or not they are going to fit. The least squares averaging method may indicate that the piston will fit into the cylinder while in reality, due to the fact that the parts have form errors, e.g., cylindricity errors, they may not fit at all. The proper evaluation for the purpose of the fit would be to use maximum inscribed cylinder for the cylinder and minimum circumscribed cylinder for the piston.
Thus, there is a need in the art for a data reduction method in which the result of a comparison to a tolerance zone with the full data set and with a reduced data set produces the same conclusion as to whether the part is in or out of tolerance.